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Powers of Linear Forms
Algebra & Discrete Mathematics| Speaker: | Bernd Sturmfels, UC Berkeley, Mathematics |
| Location: | 2112 MSB |
| Start time: | Fri, Feb 20 2009, 2:10PM |
Description
What is the dimension of the space of polynomials of a certain
degree that are annihilated by certain powers of fixed vector fields? We
obtain explicit formulas by computing sagbi bases of Cox-Nagata rings. They
count the number of lattice points in certain polytopes derived from root
systems. For del Pezzo surfaces, Cox-Nagata rings are presented by quadratic
polynomials, and, for the blow-up of projective n-space at n+3 points,
this involves a beautiful connection between the Verlinde formula and
phylogenetic algebraic geometry. This is joint work with Zhiqiang Xu.
Paper: arXiv:0803.0892